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Graduate Student Geometry-Topology Seminar

Wednesday, March 22, 2023 - 12:00pm

Jacob van Hook



University of Pennsylvania


Symmetric spaces are manifolds with isometries that reverse all directions at any given point. They are important to things such as holonomy and representation theory, and have applications in other fields such as homotopy theory. The curvature tensor of a symmetric space satisfies R(X,Y)⋅R = 0 and so we may consider spaces with this property, which we call semisymmetric spaces. I will discuss examples and properties of symmetric spaces and semisymmetric spaces including classification and structure theorems.